//headers 
#include<algorithm>
#include<cassert>
#include<cstdio>
#include<deque>
#include<iostream>
#include<list>
#include<map>
#include<numeric>
#include<deque>
#include<set>
#include<string>
#include<sstream>
#include<stack>
#include<streambuf>
#include<vector>
using namespace std;

//macros
#define LET(x,a) typeof(a) x(a)
#define FOR(i,a,n) for(LET(i,a);i!=n;i++)
#define REP(i,n) FOR(i,0,n)
#define sz size()
#define pb push_back
#define ALL(x) x.begin(),x.end()
#define dbge(x) cout<<#x<<"->"<<x<<endl;
#define PRINT(x) { REP(tmp,x.sz) cout<<x[tmp]<<" "; cout<<endl; }
#define LL long long
#define VI vector<int>
#define VS vector<string>
#define VVI vector< VI >
const int INF = (int)(1e8);

//code of suren
//the power of cryptography problem ! 

int main(){
  int 
}
